LMFDB - Embedded newform 400.2.y.c.209.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(129,400)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("400.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.y (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			209.1
Root			$1.66637 - 0.917186i$ of defining polynomial
Character	$\chi$	$=$	400.209
Dual form			400.2.y.c.289.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.451659 - 0.146753i) q^{3} +(2.19625 + 0.420099i) q^{5} +3.03582i q^{7} +(-2.24459 + 1.63079i) q^{9} +O(q^{10})$	\(q+(0.451659 - 0.146753i) q^{3} +(2.19625 + 0.420099i) q^{5} +3.03582i q^{7} +(-2.24459 + 1.63079i) q^{9} +(1.61803 + 1.17557i) q^{11} +(0.838893 + 1.15464i) q^{13} +(1.05361 - 0.132565i) q^{15} +(-1.76920 - 0.574848i) q^{17} +(0.279141 - 0.859107i) q^{19} +(0.445515 + 1.37116i) q^{21} +(1.95693 - 2.69348i) q^{23} +(4.64703 + 1.84529i) q^{25} +(-1.61189 + 2.21858i) q^{27} +(-1.22466 - 3.76910i) q^{29} +(1.99006 - 6.12477i) q^{31} +(0.903319 + 0.293506i) q^{33} +(-1.27534 + 6.66742i) q^{35} +(2.24547 + 3.09062i) q^{37} +(0.548341 + 0.398393i) q^{39} +(1.48391 - 1.07813i) q^{41} +3.59445i q^{43} +(-5.61478 + 2.63868i) q^{45} +(4.56502 - 1.48326i) q^{47} -2.21619 q^{49} -0.883436 q^{51} +(9.03953 - 2.93712i) q^{53} +(3.05975 + 3.26158i) q^{55} -0.428989i q^{57} +(-8.61248 + 6.25734i) q^{59} +(-11.5481 - 8.39016i) q^{61} +(-4.95078 - 6.81417i) q^{63} +(1.35736 + 2.88829i) q^{65} +(-10.1670 - 3.30345i) q^{67} +(0.488588 - 1.50372i) q^{69} +(-3.85030 - 11.8500i) q^{71} +(0.157310 - 0.216518i) q^{73} +(2.36968 + 0.151474i) q^{75} +(-3.56882 + 4.91206i) q^{77} +(-2.64882 - 8.15223i) q^{79} +(2.16963 - 6.67743i) q^{81} +(12.0006 + 3.89923i) q^{83} +(-3.64411 - 2.00575i) q^{85} +(-1.10626 - 1.52263i) q^{87} +(-3.85736 - 2.80253i) q^{89} +(-3.50527 + 2.54673i) q^{91} -3.05836i q^{93} +(0.973973 - 1.76955i) q^{95} +(-9.47067 + 3.07721i) q^{97} -5.54893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} + q^{9}+O(q^{10}) $ 8 * q + 5 * q^3 + q^9	$ 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q + 5 * q^3 + q^9 + 4 * q^11 - 5 * q^13 - 15 * q^15 - 10 * q^17 + 5 * q^19 - 4 * q^21 - 5 * q^23 - 10 * q^25 + 5 * q^27 - 5 * q^29 + 9 * q^31 + 10 * q^33 - 15 * q^35 + 30 * q^37 + 3 * q^39 - 4 * q^41 - 15 * q^45 + 14 * q^49 + 4 * q^51 - 10 * q^53 + 10 * q^55 - 9 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 + 17 * q^69 - 6 * q^71 + 15 * q^73 + 10 * q^75 + 10 * q^77 - 15 * q^79 + 28 * q^81 + 45 * q^83 - 15 * q^85 + 20 * q^87 - 25 * q^89 - 6 * q^91 - 15 * q^95 - 60 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.451659	−	0.146753i	0.260766	−	0.0847279i	−0.175716	−	0.984441i	$-0.556224\pi$
$3$	0.451659	−	0.146753i	0.260766	−	0.0847279i	0.436482	+	0.899713i	$0.356224\pi$
$4$		0			0
$5$	2.19625	+	0.420099i	0.982193	+	0.187874i
$5$	2.19625	+	0.420099i	0.982193	+	0.187874i
$6$		0			0
$7$			3.03582i			1.14743i	0.819055	+	0.573716i	$0.194498\pi$
$7$			3.03582i			1.14743i	−0.819055	+	0.573716i	$0.805502\pi$
$8$		0			0
$9$	−2.24459	+	1.63079i	−0.748197	+	0.543597i
$10$		0			0
$11$	1.61803	+	1.17557i	0.487856	+	0.354448i	0.804359	−	0.594144i	$-0.202509\pi$
$11$	1.61803	+	1.17557i	0.487856	+	0.354448i	−0.316503	+	0.948591i	$0.602509\pi$
$12$		0			0
$13$	0.838893	+	1.15464i	0.232667	+	0.320239i	0.909347	−	0.416039i	$-0.136582\pi$
$13$	0.838893	+	1.15464i	0.232667	+	0.320239i	−0.676680	+	0.736277i	$0.736582\pi$
$14$		0			0
$15$	1.05361	−	0.132565i	0.272040	−	0.0342281i
$16$		0			0
$17$	−1.76920	−	0.574848i	−0.429094	−	0.139421i	0.0865044	−	0.996251i	$-0.472430\pi$
$17$	−1.76920	−	0.574848i	−0.429094	−	0.139421i	−0.515598	+	0.856830i	$0.672430\pi$
$18$		0			0
$19$	0.279141	−	0.859107i	0.0640393	−	0.197093i	−0.913918	−	0.405900i	$-0.866958\pi$
$19$	0.279141	−	0.859107i	0.0640393	−	0.197093i	0.977957	+	0.208807i	$0.0669581\pi$
$20$		0			0
$21$	0.445515	+	1.37116i	0.0972194	+	0.299211i
$22$		0			0
$23$	1.95693	−	2.69348i	0.408048	−	0.561629i	−0.554693	−	0.832055i	$-0.687164\pi$
$23$	1.95693	−	2.69348i	0.408048	−	0.561629i	0.962741	+	0.270426i	$0.0871644\pi$
$24$		0			0
$25$	4.64703	+	1.84529i	0.929407	+	0.369057i
$26$		0			0
$27$	−1.61189	+	2.21858i	−0.310208	+	0.426965i
$28$		0			0
$29$	−1.22466	−	3.76910i	−0.227413	−	0.699905i	−0.998038	−	0.0626159i	$-0.980056\pi$
$29$	−1.22466	−	3.76910i	−0.227413	−	0.699905i	0.770625	−	0.637289i	$-0.219944\pi$
$30$		0			0
$31$	1.99006	−	6.12477i	0.357425	−	1.10004i	−0.597165	−	0.802119i	$-0.703706\pi$
$31$	1.99006	−	6.12477i	0.357425	−	1.10004i	0.954590	−	0.297923i	$-0.0962938\pi$
$32$		0			0
$33$	0.903319	+	0.293506i	0.157248	+	0.0510929i
$34$		0			0
$35$	−1.27534	+	6.66742i	−0.215572	+	1.12700i
$36$		0			0
$37$	2.24547	+	3.09062i	0.369153	+	0.508095i	0.952670	−	0.304005i	$-0.0983241\pi$
$37$	2.24547	+	3.09062i	0.369153	+	0.508095i	−0.583518	+	0.812100i	$0.698324\pi$
$38$		0			0
$39$	0.548341	+	0.398393i	0.0878048	+	0.0637939i
$40$		0			0
$41$	1.48391	−	1.07813i	0.231749	−	0.168375i	−0.465851	−	0.884863i	$-0.654252\pi$
$41$	1.48391	−	1.07813i	0.231749	−	0.168375i	0.697599	+	0.716488i	$0.254252\pi$
$42$		0			0
$43$			3.59445i			0.548149i	0.961708	+	0.274074i	$0.0883715\pi$
$43$			3.59445i			0.548149i	−0.961708	+	0.274074i	$0.911629\pi$
$44$		0			0
$45$	−5.61478	+	2.63868i	−0.837002	+	0.393350i
$46$		0			0
$47$	4.56502	−	1.48326i	0.665877	−	0.216356i	0.0434750	−	0.999055i	$-0.486157\pi$
$47$	4.56502	−	1.48326i	0.665877	−	0.216356i	0.622402	+	0.782698i	$0.286157\pi$
$48$		0			0
$49$	−2.21619			−0.316598
$50$		0			0
$51$	−0.883436			−0.123706
$52$		0			0
$53$	9.03953	−	2.93712i	1.24168	−	0.403445i	0.386745	−	0.922187i	$-0.373599\pi$
$53$	9.03953	−	2.93712i	1.24168	−	0.403445i	0.854931	+	0.518742i	$0.173599\pi$
$54$		0			0
$55$	3.05975	+	3.26158i	0.412577	+	0.439792i
$56$		0			0
$57$		−	0.428989i		−	0.0568209i
$58$		0			0
$59$	−8.61248	+	6.25734i	−1.12125	+	0.814636i	−0.984398	−	0.175956i	$-0.943698\pi$
$59$	−8.61248	+	6.25734i	−1.12125	+	0.814636i	−0.136852	+	0.990592i	$0.543698\pi$
$60$		0			0
$61$	−11.5481	−	8.39016i	−1.47858	−	1.07425i	−0.978012	−	0.208551i	$-0.933125\pi$
$61$	−11.5481	−	8.39016i	−1.47858	−	1.07425i	−0.500566	−	0.865698i	$-0.666875\pi$
$62$		0			0
$63$	−4.95078	−	6.81417i	−0.623740	−	0.858505i
$64$		0			0
$65$	1.35736	+	2.88829i	0.168359	+	0.358248i
$66$		0			0
$67$	−10.1670	−	3.30345i	−1.24209	−	0.403580i	−0.387012	−	0.922075i	$-0.626493\pi$
$67$	−10.1670	−	3.30345i	−1.24209	−	0.403580i	−0.855081	+	0.518494i	$0.826493\pi$
$68$		0			0
$69$	0.488588	−	1.50372i	0.0588191	−	0.181027i
$70$		0			0
$71$	−3.85030	−	11.8500i	−0.456947	−	1.40634i	−0.868834	−	0.495104i	$-0.835130\pi$
$71$	−3.85030	−	11.8500i	−0.456947	−	1.40634i	0.411887	−	0.911235i	$-0.364870\pi$
$72$		0			0
$73$	0.157310	−	0.216518i	0.0184117	−	0.0253415i	−0.799712	−	0.600384i	$-0.795014\pi$
$73$	0.157310	−	0.216518i	0.0184117	−	0.0253415i	0.818124	+	0.575042i	$0.195014\pi$
$74$		0			0
$75$	2.36968	+	0.151474i	0.273627	+	0.0174907i
$76$		0			0
$77$	−3.56882	+	4.91206i	−0.406704	+	0.559781i
$78$		0			0
$79$	−2.64882	−	8.15223i	−0.298015	−	0.917197i	−0.982192	−	0.187881i	$-0.939838\pi$
$79$	−2.64882	−	8.15223i	−0.298015	−	0.917197i	0.684176	−	0.729316i	$-0.260162\pi$
$80$		0			0
$81$	2.16963	−	6.67743i	0.241070	−	0.741937i
$82$		0			0
$83$	12.0006	+	3.89923i	1.31724	+	0.427996i	0.881545	−	0.472100i	$-0.156504\pi$
$83$	12.0006	+	3.89923i	1.31724	+	0.427996i	0.435691	+	0.900096i	$0.356504\pi$
$84$		0			0
$85$	−3.64411	−	2.00575i	−0.395260	−	0.217554i
$86$		0			0
$87$	−1.10626	−	1.52263i	−0.118603	−	0.163243i
$88$		0			0
$89$	−3.85736	−	2.80253i	−0.408879	−	0.297068i	0.364269	−	0.931294i	$-0.381319\pi$
$89$	−3.85736	−	2.80253i	−0.408879	−	0.297068i	−0.773148	+	0.634226i	$0.781319\pi$
$90$		0			0
$91$	−3.50527	+	2.54673i	−0.367452	+	0.266969i
$92$		0			0
$93$		−	3.05836i		−	0.317137i
$94$		0			0
$95$	0.973973	−	1.76955i	0.0999276	−	0.181552i
$96$		0			0
$97$	−9.47067	+	3.07721i	−0.961600	+	0.312443i	−0.747420	−	0.664351i	$-0.768708\pi$
$97$	−9.47067	+	3.07721i	−0.961600	+	0.312443i	−0.214180	+	0.976794i	$0.568708\pi$
$98$		0			0
$99$	−5.54893			−0.557689
$100$		0			0
$101$	9.34612			0.929974			0.464987	−	0.885318i	$-0.346059\pi$
$101$	9.34612			0.929974			0.464987	+	0.885318i	$0.346059\pi$
$102$		0			0
$103$	8.63947	−	2.80713i	0.851272	−	0.276595i	0.149294	−	0.988793i	$-0.452300\pi$
$103$	8.63947	−	2.80713i	0.851272	−	0.276595i	0.701979	+	0.712198i	$0.252300\pi$
$104$		0			0
$105$	0.402443	+	3.19856i	0.0392744	+	0.312148i
$106$		0			0
$107$			5.62871i			0.544148i	0.962276	+	0.272074i	$0.0877096\pi$
$107$			5.62871i			0.544148i	−0.962276	+	0.272074i	$0.912290\pi$
$108$		0			0
$109$	−8.18158	+	5.94427i	−0.783654	+	0.569358i	−0.906073	−	0.423121i	$-0.860935\pi$
$109$	−8.18158	+	5.94427i	−0.783654	+	0.569358i	0.122420	+	0.992478i	$0.460935\pi$
$110$		0			0
$111$	1.46774	+	1.06638i	0.139312	+	0.101216i
$112$		0			0
$113$	−6.29636	−	8.66620i	−0.592312	−	0.815247i	0.402666	−	0.915347i	$-0.368084\pi$
$113$	−6.29636	−	8.66620i	−0.592312	−	0.815247i	−0.994977	+	0.100100i	$0.968084\pi$
$114$		0			0
$115$	5.42943	−	5.09345i	0.506297	−	0.474967i
$116$		0			0
$117$	−3.76594	−	1.22363i	−0.348162	−	0.113125i
$118$		0			0
$119$	1.74513	−	5.37097i	0.159976	−	0.492356i
$120$		0			0
$121$	−2.16312	−	6.65740i	−0.196647	−	0.605218i
$122$		0			0
$123$	0.512006	−	0.704715i	0.0461660	−	0.0635420i
$124$		0			0
$125$	9.43085	+	6.00492i	0.843521	+	0.537097i
$126$		0			0
$127$	−6.67779	+	9.19118i	−0.592558	+	0.815586i	−0.995002	−	0.0998589i	$-0.968161\pi$
$127$	−6.67779	+	9.19118i	−0.592558	+	0.815586i	0.402444	+	0.915445i	$0.368161\pi$
$128$		0			0
$129$	0.527497	+	1.62347i	0.0464435	+	0.142938i
$130$		0			0
$131$	−2.46834	+	7.59677i	−0.215660	+	0.663732i	0.783446	+	0.621459i	$0.213460\pi$
$131$	−2.46834	+	7.59677i	−0.215660	+	0.663732i	−0.999106	+	0.0422730i	$0.986540\pi$
$132$		0			0
$133$	2.60809	+	0.847421i	0.226150	+	0.0734807i
$134$		0			0
$135$	−4.47214	+	4.19540i	−0.384900	+	0.361082i
$136$		0			0
$137$	5.48831	+	7.55401i	0.468898	+	0.645382i	0.976324	−	0.216313i	$-0.0694031\pi$
$137$	5.48831	+	7.55401i	0.468898	+	0.645382i	−0.507426	+	0.861695i	$0.669403\pi$
$138$		0			0
$139$	−14.4936	−	10.5302i	−1.22933	−	0.893160i	−0.232489	−	0.972599i	$-0.574687\pi$
$139$	−14.4936	−	10.5302i	−1.22933	−	0.893160i	−0.996840	+	0.0794393i	$0.974687\pi$
$140$		0			0
$141$	1.84416	−	1.33986i	0.155306	−	0.112837i
$142$		0			0
$143$			2.85442i			0.238699i
$144$		0			0
$145$	−1.10626	−	8.79238i	−0.0918695	−	0.730167i
$146$		0			0
$147$	−1.00096	+	0.325232i	−0.0825579	+	0.0268247i
$148$		0			0
$149$	6.31395			0.517259			0.258629	−	0.965977i	$-0.416729\pi$
$149$	6.31395			0.517259			0.258629	+	0.965977i	$0.416729\pi$
$150$		0			0
$151$	−4.71947			−0.384065			−0.192033	−	0.981389i	$-0.561508\pi$
$151$	−4.71947			−0.384065			−0.192033	+	0.981389i	$0.561508\pi$
$152$		0			0
$153$	4.90859	−	1.59490i	0.396836	−	0.128940i
$154$		0			0
$155$	6.94368	−	12.6155i	0.557730	−	1.01330i
$156$		0			0
$157$		−	1.46908i		−	0.117245i	−0.998280	−	0.0586225i	$-0.981329\pi$
$157$		−	1.46908i		−	0.117245i	0.998280	−	0.0586225i	$-0.0186708\pi$
$158$		0			0
$159$	3.65176	−	2.65316i	0.289603	−	0.210409i
$160$		0			0
$161$	8.17691	+	5.94087i	0.644431	+	0.468206i
$162$		0			0
$163$	2.62134	+	3.60797i	0.205319	+	0.282598i	0.899242	−	0.437452i	$-0.144119\pi$
$163$	2.62134	+	3.60797i	0.205319	+	0.282598i	−0.693922	+	0.720050i	$0.744119\pi$
$164$		0			0
$165$	1.86061	+	1.02410i	0.144849	+	0.0797258i
$166$		0			0
$167$	9.92300	+	3.22418i	0.767865	+	0.249494i	0.666651	−	0.745370i	$-0.267727\pi$
$167$	9.92300	+	3.22418i	0.767865	+	0.249494i	0.101214	+	0.994865i	$0.467727\pi$
$168$		0			0
$169$	3.38778	−	10.4265i	0.260598	−	0.802038i
$170$		0			0
$171$	0.774467	+	2.38357i	0.0592250	+	0.182276i
$172$		0			0
$173$	−4.51195	+	6.21017i	−0.343037	+	0.472151i	−0.945326	−	0.326128i	$-0.894256\pi$
$173$	−4.51195	+	6.21017i	−0.343037	+	0.472151i	0.602288	+	0.798279i	$0.294256\pi$
$174$		0			0
$175$	−5.60195	+	14.1075i	−0.423468	+	1.06643i
$176$		0			0
$177$	−2.97163	+	4.09009i	−0.223361	+	0.307430i
$178$		0			0
$179$	4.79494	+	14.7573i	0.358391	+	1.10301i	0.954017	+	0.299752i	$0.0969040\pi$
$179$	4.79494	+	14.7573i	0.358391	+	1.10301i	−0.595626	+	0.803262i	$0.703096\pi$
$180$		0			0
$181$	−0.491509	+	1.51271i	−0.0365336	+	0.112439i	−0.967660	−	0.252257i	$-0.918827\pi$
$181$	−0.491509	+	1.51271i	−0.0365336	+	0.112439i	0.931127	+	0.364696i	$0.118827\pi$
$182$		0			0
$183$	−6.44707	−	2.09478i	−0.476581	−	0.154851i
$184$		0			0
$185$	3.63324	+	7.73110i	0.267121	+	0.568402i
$186$		0			0
$187$	−2.18685	−	3.00994i	−0.159918	−	0.220109i
$188$		0			0
$189$	−6.73519	−	4.89340i	−0.489913	−	0.355943i
$190$		0			0
$191$	15.9121	−	11.5608i	1.15136	−	0.836511i	0.162698	−	0.986676i	$-0.447980\pi$
$191$	15.9121	−	11.5608i	1.15136	−	0.836511i	0.988661	+	0.150164i	$0.0479803\pi$
$192$		0			0
$193$			13.1100i			0.943680i	0.881684	+	0.471840i	$0.156410\pi$
$193$			13.1100i			0.943680i	−0.881684	+	0.471840i	$0.843590\pi$
$194$		0			0
$195$	1.03693	+	1.10533i	0.0742560	+	0.0791542i
$196$		0			0
$197$	−3.26164	+	1.05977i	−0.232382	+	0.0755055i	−0.422893	−	0.906180i	$-0.638985\pi$
$197$	−3.26164	+	1.05977i	−0.232382	+	0.0755055i	0.190511	+	0.981685i	$0.438985\pi$
$198$		0			0
$199$	17.6959			1.25443			0.627215	−	0.778846i	$-0.284195\pi$
$199$	17.6959			1.25443			0.627215	+	0.778846i	$0.284195\pi$
$200$		0			0
$201$	−5.07680			−0.358090
$202$		0			0
$203$	11.4423	−	3.71783i	0.803093	−	0.260941i
$204$		0			0
$205$	3.71197	−	1.74445i	0.259255	−	0.121837i
$206$		0			0
$207$			9.23710i			0.642023i
$208$		0			0
$209$	1.46160	−	1.06192i	0.101101	−	0.0734542i
$210$		0			0
$211$	−2.62418	−	1.90658i	−0.180656	−	0.131254i	0.493782	−	0.869586i	$-0.335614\pi$
$211$	−2.62418	−	1.90658i	−0.180656	−	0.131254i	−0.674438	+	0.738331i	$0.735614\pi$
$212$		0			0
$213$	−3.47805	−	4.78713i	−0.238312	−	0.328009i
$214$		0			0
$215$	−1.51003	+	7.89432i	−0.102983	+	0.538388i
$216$		0			0
$217$	18.5937	+	6.04145i	1.26222	+	0.410121i
$218$		0			0
$219$	0.0392757	−	0.120878i	0.00265401	−	0.00816819i
$220$		0			0
$221$	−0.820429	−	2.52502i	−0.0551880	−	0.169851i
$222$		0			0
$223$	−16.8781	+	23.2307i	−1.13024	+	1.55564i	−0.342633	+	0.939469i	$0.611319\pi$
$223$	−16.8781	+	23.2307i	−1.13024	+	1.55564i	−0.787609	+	0.616175i	$0.788681\pi$
$224$		0			0
$225$	−13.4400	+	3.43643i	−0.895998	+	0.229095i
$226$		0			0
$227$	6.88921	−	9.48219i	0.457253	−	0.629355i	−0.516683	−	0.856177i	$-0.672833\pi$
$227$	6.88921	−	9.48219i	0.457253	−	0.629355i	0.973936	+	0.226822i	$0.0728335\pi$
$228$		0			0
$229$	5.06828	+	15.5985i	0.334921	+	1.03078i	0.966761	+	0.255682i	$0.0823000\pi$
$229$	5.06828	+	15.5985i	0.334921	+	1.03078i	−0.631840	+	0.775099i	$0.717700\pi$
$230$		0			0
$231$	−0.891031	+	2.74231i	−0.0586255	+	0.180431i
$232$		0			0
$233$	21.4126	+	6.95739i	1.40279	+	0.455794i	0.910092	−	0.414407i	$-0.136011\pi$
$233$	21.4126	+	6.95739i	1.40279	+	0.455794i	0.492697	+	0.870201i	$0.336011\pi$
$234$		0			0
$235$	10.6490	−	1.33986i	0.694667	−	0.0874029i
$236$		0			0
$237$	−2.39273	−	3.29331i	−0.155424	−	0.213923i
$238$		0			0
$239$	5.36647	+	3.89897i	0.347128	+	0.252204i	0.747663	−	0.664078i	$-0.231176\pi$
$239$	5.36647	+	3.89897i	0.347128	+	0.252204i	−0.400535	+	0.916281i	$0.631176\pi$
$240$		0			0
$241$	−21.2173	+	15.4153i	−1.36673	+	0.992986i	−0.368743	+	0.929531i	$0.620212\pi$
$241$	−21.2173	+	15.4153i	−1.36673	+	0.992986i	−0.997985	+	0.0634545i	$0.979788\pi$
$242$		0			0
$243$		−	11.5613i		−	0.741655i
$244$		0			0
$245$	−4.86730	−	0.931017i	−0.310960	−	0.0594805i
$246$		0			0
$247$	1.22613	−	0.398393i	0.0780166	−	0.0253491i
$248$		0			0
$249$	5.99241			0.379753
$250$		0			0
$251$	10.9121			0.688766			0.344383	−	0.938829i	$-0.388088\pi$
$251$	10.9121			0.688766			0.344383	+	0.938829i	$0.388088\pi$
$252$		0			0
$253$	6.33275	−	2.05763i	0.398137	−	0.129362i
$254$		0			0
$255$	−1.94025	−	0.371131i	−0.121503	−	0.0232411i
$256$		0			0
$257$		−	6.58051i		−	0.410481i	−0.978712	−	0.205240i	$-0.934202\pi$
$257$		−	6.58051i		−	0.410481i	0.978712	−	0.205240i	$-0.0657976\pi$
$258$		0			0
$259$	−9.38256	+	6.81683i	−0.583004	+	0.423577i
$260$		0			0
$261$	8.89547	+	6.46294i	0.550616	+	0.400046i
$262$		0			0
$263$	−15.9332	−	21.9302i	−0.982486	−	1.35228i	−0.935479	−	0.353382i	$-0.885032\pi$
$263$	−15.9332	−	21.9302i	−0.982486	−	1.35228i	−0.0470069	−	0.998895i	$-0.514968\pi$
$264$		0			0
$265$	21.0870	−	2.65316i	1.29536	−	0.162982i
$266$		0			0
$267$	−2.15349	−	0.699712i	−0.131792	−	0.0428217i
$268$		0			0
$269$	−0.311938	+	0.960046i	−0.0190192	+	0.0585350i	−0.960116	−	0.279603i	$-0.909797\pi$
$269$	−0.311938	+	0.960046i	−0.0190192	+	0.0585350i	0.941096	+	0.338138i	$0.109797\pi$
$270$		0			0
$271$	−1.93198	−	5.94603i	−0.117360	−	0.361196i	0.875072	−	0.483992i	$-0.160814\pi$
$271$	−1.93198	−	5.94603i	−0.117360	−	0.361196i	−0.992432	+	0.122796i	$0.960814\pi$
$272$		0			0
$273$	−1.20945	+	1.66466i	−0.0731991	+	0.100750i
$274$		0			0
$275$	5.34980	+	8.44865i	0.322605	+	0.509473i
$276$		0			0
$277$	14.5009	−	19.9587i	0.871272	−	1.19920i	−0.107491	−	0.994206i	$-0.534282\pi$
$277$	14.5009	−	19.9587i	0.871272	−	1.19920i	0.978763	−	0.204997i	$-0.0657184\pi$
$278$		0			0
$279$	5.52135	+	16.9930i	0.330555	+	1.01734i
$280$		0			0
$281$	0.568255	−	1.74891i	0.0338993	−	0.104331i	−0.932675	−	0.360717i	$-0.882532\pi$
$281$	0.568255	−	1.74891i	0.0338993	−	0.104331i	0.966574	+	0.256386i	$0.0825319\pi$
$282$		0			0
$283$	8.21823	+	2.67026i	0.488523	+	0.158731i	0.542913	−	0.839789i	$-0.317321\pi$
$283$	8.21823	+	2.67026i	0.488523	+	0.158731i	−0.0543898	+	0.998520i	$0.517321\pi$
$284$		0			0
$285$	0.180218	−	0.942167i	0.0106752	−	0.0558091i
$286$		0			0
$287$	3.27300	+	4.50489i	0.193199	+	0.265915i
$288$		0			0
$289$	−10.9537	−	7.95831i	−0.644334	−	0.468136i
$290$		0			0
$291$	−3.82593	+	2.77970i	−0.224280	+	0.162949i
$292$		0			0
$293$			6.29156i			0.367557i	0.982968	+	0.183779i	$0.0588329\pi$
$293$			6.29156i			0.367557i	−0.982968	+	0.183779i	$0.941167\pi$
$294$		0			0
$295$	−21.5439	+	10.1246i	−1.25433	+	0.589476i
$296$		0			0
$297$	−5.21619	+	1.69484i	−0.302674	+	0.0983447i
$298$		0			0
$299$	4.75164			0.274795
$300$		0			0
$301$	−10.9121			−0.628963
$302$		0			0
$303$	4.22126	−	1.37157i	0.242505	−	0.0787947i
$304$		0			0
$305$	−21.8377	−	23.2782i	−1.25043	−	1.33291i
$306$		0			0
$307$		−	28.6661i		−	1.63606i	−0.575175	−	0.818030i	$-0.695066\pi$
$307$		−	28.6661i		−	1.63606i	0.575175	−	0.818030i	$-0.304934\pi$
$308$		0			0
$309$	3.49014	−	2.53574i	0.198547	−	0.144253i
$310$		0			0
$311$	−6.33985	−	4.60617i	−0.359500	−	0.261192i	0.393343	−	0.919392i	$-0.371318\pi$
$311$	−6.33985	−	4.60617i	−0.359500	−	0.261192i	−0.752844	+	0.658199i	$0.771318\pi$
$312$		0			0
$313$	−12.5840	−	17.3205i	−0.711292	−	0.979010i	−0.999768	−	0.0215228i	$-0.993149\pi$
$313$	−12.5840	−	17.3205i	−0.711292	−	0.979010i	0.288476	−	0.957487i	$-0.406851\pi$
$314$		0			0
$315$	−8.01054	−	17.0454i	−0.451343	−	0.960402i
$316$		0			0
$317$	−3.82309	−	1.24220i	−0.214726	−	0.0697688i	0.199679	−	0.979861i	$-0.436010\pi$
$317$	−3.82309	−	1.24220i	−0.214726	−	0.0697688i	−0.414405	+	0.910093i	$0.636010\pi$
$318$		0			0
$319$	2.44931	−	7.53821i	0.137135	−	0.422059i
$320$		0			0
$321$	0.826031	+	2.54226i	0.0461046	+	0.141895i
$322$		0			0
$323$	−0.987712	+	1.35947i	−0.0549578	+	0.0756429i
$324$		0			0
$325$	1.76773	+	6.91364i	0.0980560	+	0.383499i
$326$		0			0
$327$	−2.82295	+	3.88546i	−0.156109	+	0.214866i
$328$		0			0
$329$	4.50292	+	13.8586i	0.248254	+	0.764047i
$330$		0			0
$331$	−3.59815	+	11.0740i	−0.197772	+	0.608681i	0.802161	+	0.597108i	$0.203684\pi$
$331$	−3.59815	+	11.0740i	−0.197772	+	0.608681i	−0.999933	+	0.0115724i	$0.996316\pi$
$332$		0			0
$333$	−10.0803	−	3.27529i	−0.552398	−	0.179485i
$334$		0			0
$335$	−20.9414	−	11.5263i	−1.14415	−	0.629751i
$336$		0			0
$337$	−12.6578	−	17.4220i	−0.689516	−	0.949037i	0.310483	−	0.950579i	$-0.399509\pi$
$337$	−12.6578	−	17.4220i	−0.689516	−	0.949037i	−0.999999	+	0.00154181i	$0.999509\pi$
$338$		0			0
$339$	−4.11560	−	2.99016i	−0.223529	−	0.162403i
$340$		0			0
$341$	10.4201	−	7.57063i	0.564279	−	0.409973i
$342$		0			0
$343$			14.5228i			0.784157i
$344$		0			0
$345$	1.70477	−	3.09729i	0.0917819	−	0.166753i
$346$		0			0
$347$	−14.8339	+	4.81981i	−0.796323	+	0.258741i	−0.678794	−	0.734328i	$-0.737497\pi$
$347$	−14.8339	+	4.81981i	−0.796323	+	0.258741i	−0.117529	+	0.993069i	$0.537497\pi$
$348$		0			0
$349$	−5.56598			−0.297940			−0.148970	−	0.988842i	$-0.547596\pi$
$349$	−5.56598			−0.297940			−0.148970	+	0.988842i	$0.547596\pi$
$350$		0			0
$351$	−3.91385			−0.208906
$352$		0			0
$353$	−7.62953	+	2.47898i	−0.406079	+	0.131943i	−0.504932	−	0.863159i	$-0.668483\pi$
$353$	−7.62953	+	2.47898i	−0.406079	+	0.131943i	0.0988533	+	0.995102i	$0.468483\pi$
$354$		0			0
$355$	−3.47805	−	27.6431i	−0.184596	−	1.46714i
$356$		0			0
$357$		−	2.68195i		−	0.141944i
$358$		0			0
$359$	9.98547	−	7.25487i	0.527013	−	0.382897i	−0.292226	−	0.956349i	$-0.594396\pi$
$359$	9.98547	−	7.25487i	0.527013	−	0.382897i	0.819239	+	0.573452i	$0.194396\pi$
$360$		0			0
$361$	14.7112	+	10.6883i	0.774272	+	0.562542i
$362$		0			0
$363$	−1.95399	−	2.68943i	−0.102558	−	0.141159i
$364$		0			0
$365$	0.436451	−	0.409443i	0.0228449	−	0.0214312i
$366$		0			0
$367$	25.5596	+	8.30481i	1.33420	+	0.433508i	0.887348	−	0.461100i	$-0.152545\pi$
$367$	25.5596	+	8.30481i	1.33420	+	0.433508i	0.446852	+	0.894608i	$0.352545\pi$
$368$		0			0
$369$	−1.57258	+	4.83991i	−0.0818653	+	0.251956i
$370$		0			0
$371$	8.91657	+	27.4424i	0.462925	+	1.42474i
$372$		0			0
$373$	−16.2457	+	22.3604i	−0.841173	+	1.15778i	0.144566	+	0.989495i	$0.453821\pi$
$373$	−16.2457	+	22.3604i	−0.841173	+	1.15778i	−0.985739	+	0.168280i	$0.946179\pi$
$374$		0			0
$375$	5.14077	+	1.32817i	0.265468	+	0.0685866i
$376$		0			0
$377$	3.32459	−	4.57591i	0.171225	−	0.235671i
$378$		0			0
$379$	−1.07372	−	3.30456i	−0.0551532	−	0.169744i	0.919685	−	0.392656i	$-0.128444\pi$
$379$	−1.07372	−	3.30456i	−0.0551532	−	0.169744i	−0.974839	+	0.222912i	$0.928444\pi$
$380$		0			0
$381$	−1.66725	+	5.13127i	−0.0854159	+	0.262883i
$382$		0			0
$383$	−26.0322	−	8.45837i	−1.33018	−	0.432203i	−0.444203	−	0.895926i	$-0.646513\pi$
$383$	−26.0322	−	8.45837i	−1.33018	−	0.432203i	−0.885980	+	0.463723i	$0.846513\pi$
$384$		0			0
$385$	−9.90157	+	9.28885i	−0.504631	+	0.473404i
$386$		0			0
$387$	−5.86180	−	8.06808i	−0.297972	−	0.410123i
$388$		0			0
$389$	8.80576	+	6.39776i	0.446470	+	0.324379i	0.788200	−	0.615419i	$-0.211013\pi$
$389$	8.80576	+	6.39776i	0.446470	+	0.324379i	−0.341731	+	0.939798i	$0.611013\pi$
$390$		0			0
$391$	−5.01054	+	3.64037i	−0.253394	+	0.184101i
$392$		0			0
$393$			3.79339i			0.191351i
$394$		0			0
$395$	−2.39273	−	19.0171i	−0.120391	−	0.956854i
$396$		0			0
$397$	15.4273	−	5.01264i	0.774275	−	0.251577i	0.104881	−	0.994485i	$-0.466554\pi$
$397$	15.4273	−	5.01264i	0.774275	−	0.251577i	0.669394	+	0.742908i	$0.266554\pi$
$398$		0			0
$399$	1.30233			0.0651981
$400$		0			0
$401$	3.78686			0.189107			0.0945534	−	0.995520i	$-0.469858\pi$
$401$	3.78686			0.189107			0.0945534	+	0.995520i	$0.469858\pi$
$402$		0			0
$403$	8.74134	−	2.84023i	0.435437	−	0.141482i
$404$		0			0
$405$	7.57024	−	13.7539i	0.376168	−	0.683435i
$406$		0			0
$407$			7.64044i			0.378722i
$408$		0			0
$409$	1.50142	−	1.09084i	0.0742403	−	0.0539388i	−0.550046	−	0.835134i	$-0.685390\pi$
$409$	1.50142	−	1.09084i	0.0742403	−	0.0539388i	0.624286	+	0.781196i	$0.285390\pi$
$410$		0			0
$411$	3.58742	+	2.60641i	0.176954	+	0.128565i
$412$		0			0
$413$	−18.9961	−	26.1459i	−0.934738	−	1.28656i
$414$		0			0
$415$	24.7182	+	13.6051i	1.21337	+	0.667849i
$416$		0			0
$417$	−8.09150	−	2.62909i	−0.396242	−	0.128747i
$418$		0			0
$419$	4.43353	−	13.6450i	0.216592	−	0.666602i	−0.782445	−	0.622720i	$-0.786028\pi$
$419$	4.43353	−	13.6450i	0.216592	−	0.666602i	0.999037	−	0.0438818i	$-0.0139725\pi$
$420$		0			0
$421$	4.77571	+	14.6981i	0.232754	+	0.716343i	0.997411	+	0.0719060i	$0.0229082\pi$
$421$	4.77571	+	14.6981i	0.232754	+	0.716343i	−0.764658	+	0.644437i	$0.777092\pi$
$422$		0			0
$423$	−7.82771	+	10.7739i	−0.380596	+	0.523846i
$424$		0			0
$425$	−7.16077	−	5.93602i	−0.347348	−	0.287939i
$426$		0			0
$427$	25.4710	−	35.0578i	1.23263	−	1.69657i
$428$		0			0
$429$	0.418895	+	1.28923i	0.0202244	+	0.0622444i
$430$		0			0
$431$	−3.86404	+	11.8923i	−0.186124	+	0.572832i	−0.999966	−	0.00825486i	$-0.997372\pi$
$431$	−3.86404	+	11.8923i	−0.186124	+	0.572832i	0.813842	+	0.581087i	$0.197372\pi$
$432$		0			0
$433$	−21.3941	−	6.95138i	−1.02814	−	0.334062i	−0.254084	−	0.967182i	$-0.581774\pi$
$433$	−21.3941	−	6.95138i	−1.02814	−	0.334062i	−0.774053	+	0.633120i	$0.781774\pi$
$434$		0			0
$435$	−1.78996	−	3.80881i	−0.0858219	−	0.182619i
$436$		0			0
$437$	−1.76773	−	2.43307i	−0.0845620	−	0.116390i
$438$		0			0
$439$	−9.85186	−	7.15780i	−0.470204	−	0.341623i	0.327317	−	0.944915i	$-0.393855\pi$
$439$	−9.85186	−	7.15780i	−0.470204	−	0.341623i	−0.797521	+	0.603292i	$0.793855\pi$
$440$		0			0
$441$	4.97443	−	3.61414i	0.236878	−	0.172102i
$442$		0			0
$443$			20.7101i			0.983968i	0.870604	+	0.491984i	$0.163728\pi$
$443$			20.7101i			0.983968i	−0.870604	+	0.491984i	$0.836272\pi$
$444$		0			0
$445$	−7.29438	−	7.77554i	−0.345787	−	0.368596i
$446$		0			0
$447$	2.85176	−	0.926591i	0.134883	−	0.0438263i
$448$		0			0
$449$	25.9539			1.22484			0.612420	−	0.790533i	$-0.290196\pi$
$449$	25.9539			1.22484			0.612420	+	0.790533i	$0.290196\pi$
$450$		0			0
$451$	3.66844			0.172740
$452$		0			0
$453$	−2.13159	+	0.692597i	−0.100151	+	0.0325411i
$454$		0			0
$455$	−8.76832	+	4.12069i	−0.411065	+	0.193181i
$456$		0			0
$457$			8.50150i			0.397684i	0.980032	+	0.198842i	$0.0637180\pi$
$457$			8.50150i			0.397684i	−0.980032	+	0.198842i	$0.936282\pi$
$458$		0			0
$459$	4.12710	−	2.99851i	0.192636	−	0.139959i
$460$		0			0
$461$	−11.9614	−	8.69044i	−0.557097	−	0.404754i	0.273299	−	0.961929i	$-0.411885\pi$
$461$	−11.9614	−	8.69044i	−0.557097	−	0.404754i	−0.830395	+	0.557175i	$0.811885\pi$
$462$		0			0
$463$	−13.0442	−	17.9538i	−0.606215	−	0.834384i	0.390044	−	0.920796i	$-0.372460\pi$
$463$	−13.0442	−	17.9538i	−0.606215	−	0.834384i	−0.996259	+	0.0864125i	$0.972460\pi$
$464$		0			0
$465$	1.28481	−	6.71692i	0.0595818	−	0.311490i
$466$		0			0
$467$	−27.1064	−	8.80741i	−1.25434	−	0.407558i	−0.394863	−	0.918740i	$-0.629208\pi$
$467$	−27.1064	−	8.80741i	−1.25434	−	0.407558i	−0.859473	+	0.511182i	$0.829208\pi$
$468$		0			0
$469$	10.0287	−	30.8651i	0.463081	−	1.42522i
$470$		0			0
$471$	−0.215591	−	0.663522i	−0.00993393	−	0.0305735i
$472$		0			0
$473$	−4.22553	+	5.81595i	−0.194290	+	0.267418i
$474$		0			0
$475$	2.88248	−	3.47721i	0.132257	−	0.159545i
$476$		0			0
$477$	−15.5002	+	21.3342i	−0.709707	+	0.976827i
$478$		0			0
$479$	7.74301	+	23.8305i	0.353787	+	1.08885i	0.956709	+	0.291045i	$0.0940030\pi$
$479$	7.74301	+	23.8305i	0.353787	+	1.08885i	−0.602922	+	0.797800i	$0.705997\pi$
$480$		0			0
$481$	−1.68484	+	5.18540i	−0.0768220	+	0.236434i
$482$		0			0
$483$	4.56502	+	1.48326i	0.207716	+	0.0674909i
$484$		0			0
$485$	−22.0927	+	2.77970i	−1.00318	+	0.126220i
$486$		0			0
$487$	0.860980	+	1.18504i	0.0390147	+	0.0536992i	0.828079	−	0.560612i	$-0.189434\pi$
$487$	0.860980	+	1.18504i	0.0390147	+	0.0536992i	−0.789064	+	0.614311i	$0.789434\pi$
$488$		0			0
$489$	1.71343	+	1.24488i	0.0774842	+	0.0562955i
$490$		0			0
$491$	−16.2359	+	11.7961i	−0.732715	+	0.532348i	−0.890421	−	0.455138i	$-0.849590\pi$
$491$	−16.2359	+	11.7961i	−0.732715	+	0.532348i	0.157706	+	0.987486i	$0.449590\pi$
$492$		0			0
$493$			7.37229i			0.332031i
$494$		0			0
$495$	−12.1869	−	2.33110i	−0.547758	−	0.104775i
$496$		0			0
$497$	35.9745	−	11.6888i	1.61368	−	0.524315i
$498$		0			0
$499$	0.624999			0.0279788			0.0139894	−	0.999902i	$-0.495547\pi$
$499$	0.624999			0.0279788			0.0139894	+	0.999902i	$0.495547\pi$
$500$		0			0
$501$	4.95498			0.221372
$502$		0			0
$503$	−18.3603	+	5.96563i	−0.818647	+	0.265994i	−0.688256	−	0.725468i	$-0.741623\pi$
$503$	−18.3603	+	5.96563i	−0.818647	+	0.265994i	−0.130391	+	0.991463i	$0.541623\pi$
$504$		0			0
$505$	20.5264	+	3.92630i	0.913414	+	0.174718i
$506$		0			0
$507$		−	5.20639i		−	0.231224i
$508$		0			0
$509$	−8.51099	+	6.18360i	−0.377243	+	0.274083i	−0.760208	−	0.649680i	$-0.774903\pi$
$509$	−8.51099	+	6.18360i	−0.377243	+	0.274083i	0.382965	+	0.923763i	$0.374903\pi$
$510$		0			0
$511$	0.657310	+	0.477563i	0.0290777	+	0.0211262i
$512$		0			0
$513$	1.45605	+	2.00408i	0.0642862	+	0.0884824i
$514$		0			0
$515$	20.1537	−	2.53574i	0.888079	−	0.111738i
$516$		0			0
$517$	9.13004	+	2.96653i	0.401539	+	0.130468i
$518$		0			0
$519$	−1.12650	+	3.46703i	−0.0494481	+	0.152186i
$520$		0			0
$521$	−3.09232	−	9.51719i	−0.135477	−	0.416956i	0.860187	−	0.509979i	$-0.170347\pi$
$521$	−3.09232	−	9.51719i	−0.135477	−	0.416956i	−0.995664	+	0.0930234i	$0.970347\pi$
$522$		0			0
$523$	−13.3915	+	18.4319i	−0.585571	+	0.805970i	−0.994292	−	0.106690i	$-0.965975\pi$
$523$	−13.3915	+	18.4319i	−0.585571	+	0.805970i	0.408721	+	0.912659i	$0.365975\pi$
$524$		0			0
$525$	−0.459848	+	7.19391i	−0.0200694	+	0.313968i
$526$		0			0
$527$	−7.04162	+	9.69196i	−0.306738	+	0.422188i
$528$		0			0
$529$	3.68213	+	11.3324i	0.160092	+	0.492714i
$530$		0			0
$531$	9.12710	−	28.0903i	0.396082	−	1.21902i
$532$		0			0
$533$	2.48969	+	0.808950i	0.107841	+	0.0350395i
$534$		0			0
$535$	−2.36462	+	12.3621i	−0.102231	+	0.534459i
$536$		0			0
$537$	4.33136	+	5.96161i	0.186912	+	0.257262i
$538$		0			0
$539$	−3.58586	−	2.60528i	−0.154454	−	0.112217i
$540$		0			0
$541$	−2.63658	+	1.91559i	−0.113356	+	0.0823576i	−0.643019	−	0.765850i	$-0.722318\pi$
$541$	−2.63658	+	1.91559i	−0.113356	+	0.0823576i	0.529663	+	0.848208i	$0.322318\pi$
$542$		0			0
$543$			0.755360i			0.0324156i
$544$		0			0
$545$	−20.4660	+	9.61803i	−0.876667	+	0.411991i
$546$		0			0
$547$	12.9232	−	4.19901i	0.552557	−	0.179537i	−0.0194122	−	0.999812i	$-0.506179\pi$
$547$	12.9232	−	4.19901i	0.552557	−	0.179537i	0.571970	+	0.820275i	$0.306179\pi$
$548$		0			0
$549$	39.6033			1.69023
$550$		0			0
$551$	−3.57992			−0.152510
$552$		0			0
$553$	24.7487	−	8.04133i	1.05242	−	0.341952i
$554$		0			0
$555$	2.77555	+	2.95863i	0.117816	+	0.125587i
$556$		0			0
$557$			27.6399i			1.17114i	0.810621	+	0.585571i	$0.199130\pi$
$557$			27.6399i			1.17114i	−0.810621	+	0.585571i	$0.800870\pi$
$558$		0			0
$559$	−4.15029	+	3.01536i	−0.175539	+	0.127536i
$560$		0			0
$561$	−1.42943	−	1.03854i	−0.0603506	−	0.0438473i
$562$		0			0
$563$	−0.975284	−	1.34236i	−0.0411033	−	0.0565738i	0.787971	−	0.615713i	$-0.211132\pi$
$563$	−0.975284	−	1.34236i	−0.0411033	−	0.0565738i	−0.829074	+	0.559139i	$0.811132\pi$
$564$		0			0
$565$	−10.1877	−	21.6782i	−0.428601	−	0.912010i
$566$		0			0
$567$	20.2715	+	6.58660i	0.851322	+	0.276611i
$568$		0			0
$569$	−5.52609	+	17.0076i	−0.231666	+	0.712994i	0.765880	+	0.642983i	$0.222303\pi$
$569$	−5.52609	+	17.0076i	−0.231666	+	0.712994i	−0.997546	+	0.0700110i	$0.977697\pi$
$570$		0			0
$571$	11.3942	+	35.0677i	0.476832	+	1.46754i	0.843472	+	0.537174i	$0.180508\pi$
$571$	11.3942	+	35.0677i	0.476832	+	1.46754i	−0.366640	+	0.930363i	$0.619492\pi$
$572$		0			0
$573$	5.49027	−	7.55670i	0.229359	−	0.315686i
$574$		0			0
$575$	14.0641	−	8.90560i	0.586515	−	0.371389i
$576$		0			0
$577$	13.4095	−	18.4567i	0.558247	−	0.768361i	−0.432855	−	0.901463i	$-0.642494\pi$
$577$	13.4095	−	18.4567i	0.558247	−	0.768361i	0.991102	+	0.133103i	$0.0424940\pi$
$578$		0			0
$579$	1.92394	+	5.92127i	0.0799560	+	0.246079i
$580$		0			0
$581$	−11.8373	+	36.4316i	−0.491096	+	1.51144i
$582$		0			0
$583$	18.0791	+	5.87425i	0.748759	+	0.243286i
$584$		0			0
$585$	−7.75691	−	4.26947i	−0.320709	−	0.176521i
$586$		0			0
$587$	6.51588	+	8.96834i	0.268939	+	0.370163i	0.922031	−	0.387116i	$-0.126529\pi$
$587$	6.51588	+	8.96834i	0.268939	+	0.370163i	−0.653092	+	0.757278i	$0.726529\pi$
$588$		0			0
$589$	−4.70633	−	3.41935i	−0.193921	−	0.140892i
$590$		0			0
$591$	−1.31762	+	0.957311i	−0.0541998	+	0.0393785i
$592$		0			0
$593$			11.1321i			0.457139i	0.973528	+	0.228570i	$0.0734049\pi$
$593$			11.1321i			0.457139i	−0.973528	+	0.228570i	$0.926595\pi$
$594$		0			0
$595$	6.08909	−	11.0629i	0.249628	−	0.453533i
$596$		0			0
$597$	7.99253	−	2.59693i	0.327112	−	0.106285i
$598$		0			0
$599$	36.2736			1.48210			0.741049	−	0.671451i	$-0.234329\pi$
$599$	36.2736			1.48210			0.741049	+	0.671451i	$0.234329\pi$
$600$		0			0
$601$	−15.1051			−0.616150			−0.308075	−	0.951362i	$-0.599685\pi$
$601$	−15.1051			−0.616150			−0.308075	+	0.951362i	$0.599685\pi$
$602$		0			0
$603$	28.2079	−	9.16531i	1.14872	−	0.373240i
$604$		0			0
$605$	−1.95399	−	15.5300i	−0.0794408	−	0.631386i
$606$		0			0
$607$		−	33.5066i		−	1.35999i	−0.733216	−	0.679996i	$-0.761982\pi$
$607$		−	33.5066i		−	1.35999i	0.733216	−	0.679996i	$-0.238018\pi$
$608$		0			0
$609$	4.62243	−	3.35839i	0.187310	−	0.136089i
$610$		0			0
$611$	5.54220	+	4.02664i	0.224213	+	0.162900i
$612$		0			0
$613$	16.4750	+	22.6758i	0.665418	+	0.915869i	0.999646	−	0.0266235i	$-0.00847552\pi$
$613$	16.4750	+	22.6758i	0.665418	+	0.915869i	−0.334228	+	0.942492i	$0.608476\pi$
$614$		0			0
$615$	1.42054	−	1.33264i	0.0572818	−	0.0537372i
$616$		0			0
$617$	−29.0284	−	9.43191i	−1.16864	−	0.379714i	−0.340505	−	0.940243i	$-0.610598\pi$
$617$	−29.0284	−	9.43191i	−1.16864	−	0.379714i	−0.828135	+	0.560528i	$0.810598\pi$
$618$		0			0
$619$	−6.70477	+	20.6352i	−0.269488	+	0.829398i	0.721138	+	0.692792i	$0.243619\pi$
$619$	−6.70477	+	20.6352i	−0.269488	+	0.829398i	−0.990625	+	0.136606i	$0.956381\pi$
$620$		0			0
$621$	2.82134	+	8.68318i	0.113216	+	0.348444i
$622$		0			0
$623$	8.50798	−	11.7102i	0.340865	−	0.469161i
$624$		0			0
$625$	18.1898	+	17.1502i	0.727594	+	0.686008i
$626$		0			0
$627$	0.504306	−	0.694118i	0.0201401	−	0.0277204i
$628$		0			0
$629$	−2.19604	−	6.75873i	−0.0875620	−	0.269488i
$630$		0			0
$631$	5.01463	−	15.4335i	0.199629	−	0.614396i	−0.800262	−	0.599651i	$-0.795306\pi$
$631$	5.01463	−	15.4335i	0.199629	−	0.614396i	0.999891	−	0.0147456i	$-0.00469383\pi$
$632$		0			0
$633$	−1.46503	−	0.476017i	−0.0582297	−	0.0189200i
$634$		0			0
$635$	−18.5273	+	17.3808i	−0.735233	+	0.689737i
$636$		0			0
$637$	−1.85914	−	2.55889i	−0.0736619	−	0.101387i
$638$		0			0
$639$	27.9673	+	20.3194i	1.10637	+	0.803823i
$640$		0			0
$641$	17.9419	−	13.0356i	0.708663	−	0.514874i	−0.174079	−	0.984732i	$-0.555695\pi$
$641$	17.9419	−	13.0356i	0.708663	−	0.514874i	0.882742	+	0.469858i	$0.155695\pi$
$642$		0			0
$643$			13.2767i			0.523583i	0.965124	+	0.261792i	$0.0843133\pi$
$643$			13.2767i			0.523583i	−0.965124	+	0.261792i	$0.915687\pi$
$644$		0			0
$645$	0.476498	+	3.78714i	0.0187621	+	0.149119i
$646$		0			0
$647$	10.7329	−	3.48735i	0.421956	−	0.137102i	−0.0903397	−	0.995911i	$-0.528795\pi$
$647$	10.7329	−	3.48735i	0.421956	−	0.137102i	0.512295	+	0.858809i	$0.328795\pi$
$648$		0			0
$649$	−21.2912			−0.835754
$650$		0			0
$651$	9.28462			0.363893
$652$		0			0
$653$	34.0606	−	11.0669i	1.33289	−	0.433083i	0.445989	−	0.895038i	$-0.352852\pi$
$653$	34.0606	−	11.0669i	1.33289	−	0.433083i	0.886903	+	0.461955i	$0.152852\pi$
$654$		0			0
$655$	−8.61248	+	15.6475i	−0.336518	+	0.611397i
$656$		0			0
$657$			0.742534i			0.0289690i
$658$		0			0
$659$	−32.1710	+	23.3736i	−1.25320	+	0.910506i	−0.998403	−	0.0564876i	$-0.982010\pi$
$659$	−32.1710	+	23.3736i	−1.25320	+	0.910506i	−0.254801	+	0.966994i	$0.582010\pi$
$660$		0			0
$661$	5.05420	+	3.67209i	0.196586	+	0.142828i	0.681724	−	0.731610i	$-0.261231\pi$
$661$	5.05420	+	3.67209i	0.196586	+	0.142828i	−0.485138	+	0.874438i	$0.661231\pi$
$662$		0			0
$663$	−0.741109	−	1.02005i	−0.0287823	−	0.0396154i
$664$		0			0
$665$	5.37202	+	2.95681i	0.208318	+	0.114660i
$666$		0			0
$667$	−12.5486	−	4.07728i	−0.485882	−	0.157873i
$668$		0			0
$669$	−4.21398	+	12.9693i	−0.162922	+	0.501422i
$670$		0			0
$671$	−8.82193	−	27.1511i	−0.340567	−	1.04816i
$672$		0			0
$673$	−24.3712	+	33.5441i	−0.939440	+	1.29303i	0.0166215	+	0.999862i	$0.494709\pi$
$673$	−24.3712	+	33.5441i	−0.939440	+	1.29303i	−0.956061	+	0.293166i	$0.905291\pi$
$674$		0			0
$675$	−11.5844	+	7.33540i	−0.445884	+	0.282340i
$676$		0			0
$677$	0.845914	−	1.16430i	0.0325111	−	0.0447477i	−0.792452	−	0.609934i	$-0.791196\pi$
$677$	0.845914	−	1.16430i	0.0325111	−	0.0447477i	0.824963	+	0.565187i	$0.191196\pi$
$678$		0			0
$679$	−9.34183	−	28.7512i	−0.358507	−	1.10337i
$680$		0			0
$681$	1.72004	−	5.29373i	0.0659120	−	0.202856i
$682$		0			0
$683$	8.07088	+	2.62239i	0.308824	+	0.100343i	0.459329	−	0.888266i	$-0.348090\pi$
$683$	8.07088	+	2.62239i	0.308824	+	0.100343i	−0.150505	+	0.988609i	$0.548090\pi$
$684$		0			0
$685$	8.88027	+	18.8961i	0.339298	+	0.721984i
$686$		0			0
$687$	4.57827	+	6.30145i	0.174672	+	0.240415i
$688$		0			0
$689$	10.9745	+	7.97345i	0.418096	+	0.303764i
$690$		0			0
$691$	−35.4186	+	25.7331i	−1.34739	+	0.978933i	−0.348248	+	0.937402i	$0.613223\pi$
$691$	−35.4186	+	25.7331i	−1.34739	+	0.978933i	−0.999137	+	0.0415304i	$0.986777\pi$
$692$		0			0
$693$		−	16.8456i		−	0.639910i
$694$		0			0
$695$	−27.4078	−	29.2157i	−1.03964	−	1.10821i
$696$		0			0
$697$	−3.24510	+	1.05440i	−0.122917	+	0.0399381i
$698$		0			0
$699$	10.6922			0.404418
$700$		0			0
$701$	0.840795			0.0317564			0.0158782	−	0.999874i	$-0.494946\pi$
$701$	0.840795			0.0317564			0.0158782	+	0.999874i	$0.494946\pi$
$702$		0			0
$703$	3.28198	−	1.06638i	0.123782	−	0.0402192i
$704$		0			0
$705$	4.61311	−	2.16794i	0.173740	−	0.0816494i
$706$		0			0
$707$			28.3731i			1.06708i
$708$		0			0
$709$	−10.8256	+	7.86529i	−0.406566	+	0.295387i	−0.772210	−	0.635367i	$-0.780849\pi$
$709$	−10.8256	+	7.86529i	−0.406566	+	0.295387i	0.365644	+	0.930755i	$0.380849\pi$
$710$		0			0
$711$	19.2401	+	13.9787i	0.721560	+	0.524244i
$712$		0			0
$713$	−12.6025	−	17.3459i	−0.471969	−	0.649610i
$714$		0			0
$715$	−1.19914	+	6.26902i	−0.0448453	+	0.234448i
$716$		0			0
$717$	2.99601	+	0.973461i	0.111888	+	0.0363546i
$718$		0			0
$719$	13.4159	−	41.2900i	0.500329	−	1.53986i	−0.308154	−	0.951336i	$-0.599711\pi$
$719$	13.4159	−	41.2900i	0.500329	−	1.53986i	0.808483	−	0.588519i	$-0.200289\pi$
$720$		0			0
$721$	8.52195	+	26.2279i	0.317374	+	0.976776i
$722$		0			0
$723$	−7.32076	+	10.0762i	−0.272262	+	0.374737i
$724$		0			0
$725$	1.26405	−	19.7750i	0.0469458	−	0.734425i
$726$		0			0
$727$	−18.8373	+	25.9274i	−0.698639	+	0.961593i	0.301329	+	0.953520i	$0.402570\pi$
$727$	−18.8373	+	25.9274i	−0.698639	+	0.961593i	−0.999967	+	0.00807318i	$0.997430\pi$
$728$		0			0
$729$	4.81224	+	14.8106i	0.178231	+	0.548539i
$730$		0			0
$731$	2.06626	−	6.35930i	0.0764235	−	0.235207i
$732$		0			0
$733$	7.74091	+	2.51517i	0.285917	+	0.0929001i	0.448465	−	0.893801i	$-0.351971\pi$
$733$	7.74091	+	2.51517i	0.285917	+	0.0929001i	−0.162547	+	0.986701i	$0.551971\pi$
$734$		0			0
$735$	−2.33499	+	0.293788i	−0.0861274	+	0.0108365i
$736$		0			0
$737$	−12.5671	−	17.2971i	−0.462914	−	0.637146i
$738$		0			0
$739$	5.76598	+	4.18923i	0.212105	+	0.154103i	0.688766	−	0.724984i	$-0.258153\pi$
$739$	5.76598	+	4.18923i	0.212105	+	0.154103i	−0.476661	+	0.879087i	$0.658153\pi$
$740$		0			0
$741$	0.495326	−	0.359876i	0.0181963	−	0.0132204i
$742$		0			0
$743$		−	21.9040i		−	0.803578i	−0.915732	−	0.401789i	$-0.868388\pi$
$743$		−	21.9040i		−	0.803578i	0.915732	−	0.401789i	$-0.131612\pi$
$744$		0			0
$745$	13.8670	+	2.65248i	0.508048	+	0.0971795i
$746$		0			0
$747$	−33.2953	+	10.8183i	−1.21821	+	0.395820i
$748$		0			0
$749$	−17.0877			−0.624373
$750$		0			0
$751$	−9.21909			−0.336409			−0.168205	−	0.985752i	$-0.553797\pi$
$751$	−9.21909			−0.336409			−0.168205	+	0.985752i	$0.553797\pi$
$752$		0			0
$753$	4.92855	−	1.60138i	0.179606	−	0.0583577i
$754$		0			0
$755$	−10.3651	−	1.98265i	−0.377226	−	0.0721559i
$756$		0			0
$757$		−	45.6524i		−	1.65926i	−0.558311	−	0.829632i	$-0.688550\pi$
$757$		−	45.6524i		−	1.65926i	0.558311	−	0.829632i	$-0.311450\pi$
$758$		0			0
$759$	2.55828	−	1.85870i	0.0928597	−	0.0674666i
$760$		0			0
$761$	−32.2844	−	23.4560i	−1.17031	−	0.850280i	−0.179264	−	0.983801i	$-0.557372\pi$
$761$	−32.2844	−	23.4560i	−1.17031	−	0.850280i	−0.991046	+	0.133521i	$0.957372\pi$
$762$		0			0
$763$	−18.0457	−	24.8378i	−0.653299	−	0.899188i
$764$		0			0
$765$	11.4505	−	1.44070i	0.413994	−	0.0520886i
$766$		0			0
$767$	−14.4499	−	4.69506i	−0.521756	−	0.169529i
$768$		0			0
$769$	13.7024	−	42.1717i	0.494122	−	1.52075i	−0.324198	−	0.945989i	$-0.605094\pi$
$769$	13.7024	−	42.1717i	0.494122	−	1.52075i	0.818320	−	0.574762i	$-0.194906\pi$
$770$		0			0
$771$	−0.965710	−	2.97215i	−0.0347792	−	0.107039i
$772$		0			0
$773$	−22.6264	+	31.1426i	−0.813816	+	1.12012i	0.176907	+	0.984228i	$0.443391\pi$
$773$	−22.6264	+	31.1426i	−0.813816	+	1.12012i	−0.990723	+	0.135894i	$0.956609\pi$
$774$		0			0
$775$	20.5498	−	24.7898i	0.738171	−	0.890476i
$776$		0			0
$777$	−3.23733	+	4.45580i	−0.116139	+	0.159851i
$778$		0			0
$779$	−0.512006	−	1.57579i	−0.0183445	−	0.0564586i
$780$		0			0
$781$	7.70061	−	23.7000i	0.275549	−	0.848054i
$782$		0			0
$783$	10.3361	+	3.35839i	0.369381	+	0.120019i
$784$		0			0
$785$	0.617158	−	3.22646i	0.0220273	−	0.115157i
$786$		0			0
$787$	31.1645	+	42.8942i	1.11089	+	1.52901i	0.820093	+	0.572231i	$0.193922\pi$
$787$	31.1645	+	42.8942i	1.11089	+	1.52901i	0.290801	+	0.956784i	$0.406078\pi$
$788$		0			0
$789$	−10.4147	−	7.56674i	−0.370774	−	0.269383i
$790$		0			0
$791$	26.3090	−	19.1146i	0.935440	−	0.679637i
$792$		0			0
$793$		−	20.3723i		−	0.723440i
$794$		0			0
$795$	9.13477	−	4.29290i	0.323977	−	0.152254i
$796$		0			0
$797$	−12.0564	+	3.91737i	−0.427060	+	0.138760i	−0.514658	−	0.857396i	$-0.672081\pi$
$797$	−12.0564	+	3.91737i	−0.427060	+	0.138760i	0.0875977	+	0.996156i	$0.472081\pi$
$798$		0			0
$799$	−8.92908			−0.315888
$800$		0			0
$801$	13.2285			0.467407
$802$		0			0
$803$	0.509065	−	0.165405i	0.0179645	−	0.00583702i
$804$		0			0
$805$	15.4628	+	16.4828i	0.544992	+	0.580941i
$806$		0			0
$807$			0.479392i			0.0168754i
$808$		0			0
$809$	−33.8926	+	24.6244i	−1.19160	+	0.865747i	−0.993432	−	0.114421i	$-0.963499\pi$
$809$	−33.8926	+	24.6244i	−1.19160	+	0.865747i	−0.198167	+	0.980168i	$0.563499\pi$
$810$		0			0
$811$	−27.9504	−	20.3072i	−0.981472	−	0.713081i	−0.0234348	−	0.999725i	$-0.507460\pi$
$811$	−27.9504	−	20.3072i	−0.981472	−	0.713081i	−0.958037	+	0.286644i	$0.907460\pi$
$812$		0			0
$813$	−1.74520	−	2.40206i	−0.0612068	−	0.0842439i
$814$		0			0
$815$	4.24142	+	9.02522i	0.148570	+	0.316140i
$816$		0			0
$817$	3.08802	+	1.00336i	0.108036	+	0.0351031i
$818$		0			0
$819$	3.71472	−	11.4327i	0.129803	−	0.399491i
$820$		0			0
$821$	−6.53103	−	20.1004i	−0.227935	−	0.701511i	−0.997980	−	0.0635220i	$-0.979767\pi$
$821$	−6.53103	−	20.1004i	−0.227935	−	0.701511i	0.770046	−	0.637989i	$-0.220233\pi$
$822$		0			0
$823$	−1.86747	+	2.57036i	−0.0650960	+	0.0895970i	−0.840324	−	0.542085i	$-0.817635\pi$
$823$	−1.86747	+	2.57036i	−0.0650960	+	0.0895970i	0.775228	+	0.631682i	$0.217635\pi$
$824$		0			0
$825$	3.65615	+	3.03081i	0.127291	+	0.105519i
$826$		0			0
$827$	5.72786	−	7.88372i	0.199177	−	0.274144i	−0.697732	−	0.716359i	$-0.745807\pi$
$827$	5.72786	−	7.88372i	0.199177	−	0.274144i	0.896909	+	0.442215i	$0.145807\pi$
$828$		0			0
$829$	−7.24188	−	22.2882i	−0.251521	−	0.774101i	−0.994495	−	0.104782i	$-0.966586\pi$
$829$	−7.24188	−	22.2882i	−0.251521	−	0.774101i	0.742974	−	0.669320i	$-0.233414\pi$
$830$		0			0
$831$	3.62045	−	11.1426i	0.125592	−	0.386532i
$832$		0			0
$833$	3.92087	+	1.27397i	0.135850	+	0.0441404i
$834$		0			0
$835$	20.4389	+	11.2497i	0.707318	+	0.389314i
$836$		0			0
$837$	10.3805	+	14.2876i	0.358803	+	0.493850i
$838$		0			0
$839$	−34.5304	−	25.0878i	−1.19212	−	0.866126i	−0.198634	−	0.980074i	$-0.563650\pi$
$839$	−34.5304	−	25.0878i	−1.19212	−	0.866126i	−0.993487	+	0.113948i	$0.963650\pi$
$840$		0			0
$841$	10.7551	−	7.81406i	0.370866	−	0.269450i
$842$		0			0
$843$		−	0.873305i		−	0.0300782i
$844$		0			0
$845$	11.8206	−	21.4760i	0.406640	−	0.738797i
$846$		0			0
$847$	20.2106	−	6.56683i	0.694446	−	0.225639i
$848$		0			0
$849$	4.10371			0.140839
$850$		0			0
$851$	12.7187			0.435993
$852$		0			0
$853$	−16.1309	+	5.24124i	−0.552310	+	0.179456i	−0.571858	−	0.820352i	$-0.693777\pi$
$853$	−16.1309	+	5.24124i	−0.552310	+	0.179456i	0.0195480	+	0.999809i	$0.493777\pi$
$854$		0			0
$855$	0.699591	+	5.56026i	0.0239255	+	0.190157i
$856$		0			0
$857$			39.3176i			1.34306i	0.740976	+	0.671531i	$0.234363\pi$
$857$			39.3176i			1.34306i	−0.740976	+	0.671531i	$0.765637\pi$
$858$		0			0
$859$	−0.572020	+	0.415597i	−0.0195171	+	0.0141800i	−0.597501	−	0.801868i	$-0.703840\pi$
$859$	−0.572020	+	0.415597i	−0.0195171	+	0.0141800i	0.577984	+	0.816048i	$0.303840\pi$
$860$		0			0
$861$	2.13939	+	1.55436i	0.0729101	+	0.0529723i
$862$		0			0
$863$	0.534537	+	0.735728i	0.0181959	+	0.0250445i	0.818018	−	0.575193i	$-0.195073\pi$
$863$	0.534537	+	0.735728i	0.0181959	+	0.0250445i	−0.799822	+	0.600237i	$0.795073\pi$
$864$		0			0
$865$	−12.5183	+	11.7436i	−0.425634	+	0.399295i
$866$		0			0
$867$	−6.11524	−	1.98696i	−0.207684	−	0.0674807i
$868$		0			0
$869$	5.29764	−	16.3045i	0.179710	−	0.553091i
$870$		0			0
$871$	−4.71472	−	14.5104i	−0.159752	−	0.491666i
$872$		0			0
$873$	16.2395	−	22.3517i	0.549624	−	0.756492i
$874$		0			0
$875$	−18.2298	+	28.6303i	−0.616281	+	0.967882i
$876$		0			0
$877$	−19.7856	+	27.2326i	−0.668113	+	0.919578i	−0.999716	−	0.0238407i	$-0.992411\pi$
$877$	−19.7856	+	27.2326i	−0.668113	+	0.919578i	0.331603	+	0.943419i	$0.392411\pi$
$878$		0			0
$879$	0.923306	+	2.84164i	0.0311423	+	0.0958463i
$880$		0			0
$881$	−6.15819	+	18.9529i	−0.207475	+	0.638541i	0.792128	+	0.610355i	$0.208973\pi$
$881$	−6.15819	+	18.9529i	−0.207475	+	0.638541i	−0.999603	+	0.0281862i	$0.991027\pi$
$882$		0			0
$883$	−14.8442	−	4.82317i	−0.499547	−	0.162313i	0.0483963	−	0.998828i	$-0.484589\pi$
$883$	−14.8442	−	4.82317i	−0.499547	−	0.162313i	−0.547943	+	0.836516i	$0.684589\pi$
$884$		0			0
$885$	−8.24468	+	7.73449i	−0.277142	+	0.259992i
$886$		0			0
$887$	−27.5652	−	37.9403i	−0.925550	−	1.27391i	−0.961570	−	0.274560i	$-0.911468\pi$
$887$	−27.5652	−	37.9403i	−0.925550	−	1.27391i	0.0360196	−	0.999351i	$-0.488532\pi$
$888$		0			0
$889$	−27.9028	−	20.2725i	−0.935828	−	0.679919i
$890$		0			0
$891$	11.3603	−	8.25376i	0.380585	−	0.276511i
$892$		0			0
$893$		−	4.33588i		−	0.145095i
$894$		0			0
$895$	4.33136	+	34.4251i	0.144782	+	1.15070i
$896$		0			0
$897$	2.14612	−	0.697318i	0.0716570	−	0.0232828i
$898$		0			0
$899$	−25.5220			−0.851208
$900$		0			0
$901$	−17.6811			−0.589044
$902$		0			0
$903$	−4.92855	+	1.60138i	−0.164012	+	0.0532907i
$904$		0			0
$905$	−1.71497	+	3.11581i	−0.0570074	+	0.103573i
$906$		0			0
$907$			1.43447i			0.0476308i	0.999716	+	0.0238154i	$0.00758139\pi$
$907$			1.43447i			0.0476308i	−0.999716	+	0.0238154i	$0.992419\pi$
$908$		0			0
$909$	−20.9782	+	15.2416i	−0.695804	+	0.505531i
$910$		0			0
$911$	−2.27438	−	1.65244i	−0.0753537	−	0.0547476i	0.549471	−	0.835513i	$-0.314829\pi$
$911$	−2.27438	−	1.65244i	−0.0753537	−	0.0547476i	−0.624824	+	0.780765i	$0.714829\pi$
$912$		0			0
$913$	14.8335	+	20.4166i	0.490919	+	0.675692i
$914$		0			0
$915$	−13.2794	−	7.30907i	−0.439002	−	0.241630i
$916$		0			0
$917$	−23.0624	−	7.49342i	−0.761587	−	0.247455i
$918$		0			0
$919$	0.306618	−	0.943673i	0.0101144	−	0.0311289i	−0.945872	−	0.324540i	$-0.894790\pi$
$919$	0.306618	−	0.943673i	0.0101144	−	0.0311289i	0.955986	+	0.293411i	$0.0947905\pi$
$920$		0			0
$921$	−4.20684	−	12.9473i	−0.138620	−	0.426629i
$922$		0			0
$923$	10.4525	−	14.3866i	0.344048	−	0.473541i
$924$		0			0
$925$	4.73169	+	18.5057i	0.155577	+	0.608465i
$926$		0			0
$927$	−14.8142	+	20.3900i	−0.486563	+	0.669697i
$928$		0			0
$929$	−10.2973	−	31.6918i	−0.337843	−	1.03977i	−0.965305	−	0.261127i	$-0.915906\pi$
$929$	−10.2973	−	31.6918i	−0.337843	−	1.03977i	0.627461	−	0.778648i	$-0.284094\pi$
$930$		0			0
$931$	−0.618628	+	1.90394i	−0.0202747	+	0.0623992i
$932$		0			0
$933$	−3.53943	−	1.15003i	−0.115876	−	0.0376503i
$934$		0			0
$935$	−3.53840	−	7.52928i	−0.115718	−	0.246234i
$936$		0			0
$937$	7.85724	+	10.8146i	0.256685	+	0.353296i	0.917838	−	0.396954i	$-0.129933\pi$
$937$	7.85724	+	10.8146i	0.256685	+	0.353296i	−0.661154	+	0.750251i	$0.729933\pi$
$938$		0			0
$939$	−8.22553	−	5.97620i	−0.268430	−	0.195026i
$940$		0			0
$941$	1.73924	−	1.26363i	0.0566976	−	0.0411932i	−0.559075	−	0.829117i	$-0.688844\pi$
$941$	1.73924	−	1.26363i	0.0566976	−	0.0411932i	0.615773	+	0.787924i	$0.288844\pi$
$942$		0			0
$943$		−	6.10671i		−	0.198862i
$944$		0			0
$945$	−12.7365	−	13.5766i	−0.414317	−	0.441646i
$946$		0			0
$947$	−33.2093	+	10.7903i	−1.07916	+	0.350639i	−0.794047	−	0.607856i	$-0.792030\pi$
$947$	−33.2093	+	10.7903i	−1.07916	+	0.350639i	−0.285109	+	0.958495i	$0.592030\pi$
$948$		0			0
$949$	0.381966			0.0123991
$950$		0			0
$951$	−1.90903			−0.0619046
$952$		0			0
$953$	7.87364	−	2.55830i	0.255052	−	0.0828715i	−0.178700	−	0.983904i	$-0.557189\pi$
$953$	7.87364	−	2.55830i	0.255052	−	0.0828715i	0.433752	+	0.901032i	$0.357189\pi$
$954$		0			0
$955$	39.8037	−	18.7058i	1.28802	−	0.605305i
$956$		0			0
$957$		−	3.76415i		−	0.121678i
$958$		0			0
$959$	−22.9326	+	16.6615i	−0.740532	+	0.538028i
$960$		0			0
$961$	−8.47296	−	6.15597i	−0.273321	−	0.198580i
$962$		0			0
$963$	−9.17926	−	12.6342i	−0.295797	−	0.407130i
$964$		0			0
$965$	−5.50751	+	28.7929i	−0.177293	+	0.926876i
$966$		0			0
$967$	28.0439	+	9.11201i	0.901831	+	0.293023i	0.722993	−	0.690856i	$-0.242766\pi$
$967$	28.0439	+	9.11201i	0.901831	+	0.293023i	0.178838	+	0.983878i	$0.442766\pi$
$968$		0			0
$969$	−0.246603	+	0.758967i	−0.00792204	+	0.0243815i
$970$		0			0
$971$	−6.75716	−	20.7964i	−0.216848	−	0.667388i	−0.999017	−	0.0443227i	$-0.985887\pi$
$971$	−6.75716	−	20.7964i	−0.216848	−	0.667388i	0.782170	−	0.623065i	$-0.214113\pi$
$972$		0			0
$973$	31.9678	−	43.9998i	1.02484	−	1.41057i
$974$		0			0
$975$	1.81301	+	2.86319i	0.0580627	+	0.0916954i
$976$		0			0
$977$	−8.13976	+	11.2034i	−0.260414	+	0.358429i	−0.919124	−	0.393967i	$-0.871102\pi$
$977$	−8.13976	+	11.2034i	−0.260414	+	0.358429i	0.658710	+	0.752397i	$0.271102\pi$
$978$		0			0
$979$	−2.94676	−	9.06919i	−0.0941788	−	0.289853i
$980$		0			0
$981$	8.67045	−	26.6849i	0.276826	−	0.851983i
$982$		0			0
$983$	−2.79171	−	0.907082i	−0.0890418	−	0.0289314i	0.264157	−	0.964480i	$-0.414906\pi$
$983$	−2.79171	−	0.907082i	−0.0890418	−	0.0289314i	−0.353199	+	0.935548i	$0.614906\pi$
$984$		0			0
$985$	−7.60858	+	0.957311i	−0.242430	+	0.0305025i
$986$		0			0
$987$	4.06757	+	5.59853i	0.129472	+	0.178203i
$988$		0			0
$989$	9.68158	+	7.03408i	0.307856	+	0.223671i
$990$		0			0
$991$	25.5760	−	18.5821i	0.812450	−	0.590279i	−0.102090	−	0.994775i	$-0.532553\pi$
$991$	25.5760	−	18.5821i	0.812450	−	0.590279i	0.914540	+	0.404496i	$0.132553\pi$
$992$		0			0
$993$			5.52970i			0.175480i
$994$		0			0
$995$	38.8647	+	7.43404i	1.23209	+	0.235675i
$996$		0			0
$997$	−11.4968	+	3.73554i	−0.364108	+	0.118306i	−0.485356	−	0.874316i	$-0.661310\pi$
$997$	−11.4968	+	3.73554i	−0.364108	+	0.118306i	0.121249	+	0.992622i	$0.461310\pi$
$998$		0			0
$999$	−10.4762			−0.331453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.y.c.209.1		8
4.3	odd	2		25.2.e.a.9.1	✓	8
12.11	even	2		225.2.m.a.109.2		8
20.3	even	4		125.2.d.b.76.4		16
20.7	even	4		125.2.d.b.76.1		16
20.19	odd	2		125.2.e.b.49.2		8
25.8	odd	20		10000.2.a.bj.1.5		8
25.14	even	10	inner	400.2.y.c.289.1		8
25.17	odd	20		10000.2.a.bj.1.4		8
100.3	even	20		625.2.d.o.126.1		16
100.11	odd	10		125.2.e.b.74.2		8
100.19	odd	10		625.2.b.c.624.8		8
100.23	even	20		125.2.d.b.51.4		16
100.27	even	20		125.2.d.b.51.1		16
100.31	odd	10		625.2.b.c.624.1		8
100.39	odd	10		25.2.e.a.14.1	yes	8
100.47	even	20		625.2.d.o.126.4		16
100.59	odd	10		625.2.e.a.124.2		8
100.63	even	20		625.2.d.o.501.1		16
100.67	even	20		625.2.a.f.1.8		8
100.71	odd	10		625.2.e.a.499.2		8
100.79	odd	10		625.2.e.i.499.1		8
100.83	even	20		625.2.a.f.1.1		8
100.87	even	20		625.2.d.o.501.4		16
100.91	odd	10		625.2.e.i.124.1		8
300.83	odd	20		5625.2.a.x.1.8		8
300.167	odd	20		5625.2.a.x.1.1		8
300.239	even	10		225.2.m.a.64.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.9.1	✓	8	4.3	odd	2
25.2.e.a.14.1	yes	8	100.39	odd	10
125.2.d.b.51.1		16	100.27	even	20
125.2.d.b.51.4		16	100.23	even	20
125.2.d.b.76.1		16	20.7	even	4
125.2.d.b.76.4		16	20.3	even	4
125.2.e.b.49.2		8	20.19	odd	2
125.2.e.b.74.2		8	100.11	odd	10
225.2.m.a.64.2		8	300.239	even	10
225.2.m.a.109.2		8	12.11	even	2
400.2.y.c.209.1		8	1.1	even	1	trivial
400.2.y.c.289.1		8	25.14	even	10	inner
625.2.a.f.1.1		8	100.83	even	20
625.2.a.f.1.8		8	100.67	even	20
625.2.b.c.624.1		8	100.31	odd	10
625.2.b.c.624.8		8	100.19	odd	10
625.2.d.o.126.1		16	100.3	even	20
625.2.d.o.126.4		16	100.47	even	20
625.2.d.o.501.1		16	100.63	even	20
625.2.d.o.501.4		16	100.87	even	20
625.2.e.a.124.2		8	100.59	odd	10
625.2.e.a.499.2		8	100.71	odd	10
625.2.e.i.124.1		8	100.91	odd	10
625.2.e.i.499.1		8	100.79	odd	10
5625.2.a.x.1.1		8	300.167	odd	20
5625.2.a.x.1.8		8	300.83	odd	20
10000.2.a.bj.1.4		8	25.17	odd	20
10000.2.a.bj.1.5		8	25.8	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.y (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.451659 - 0.146753i) q^{3} +(2.19625 + 0.420099i) q^{5} +3.03582i q^{7} +(-2.24459 + 1.63079i) q^{9} +O(q^{10})\)	\(q+(0.451659 - 0.146753i) q^{3} +(2.19625 + 0.420099i) q^{5} +3.03582i q^{7} +(-2.24459 + 1.63079i) q^{9} +(1.61803 + 1.17557i) q^{11} +(0.838893 + 1.15464i) q^{13} +(1.05361 - 0.132565i) q^{15} +(-1.76920 - 0.574848i) q^{17} +(0.279141 - 0.859107i) q^{19} +(0.445515 + 1.37116i) q^{21} +(1.95693 - 2.69348i) q^{23} +(4.64703 + 1.84529i) q^{25} +(-1.61189 + 2.21858i) q^{27} +(-1.22466 - 3.76910i) q^{29} +(1.99006 - 6.12477i) q^{31} +(0.903319 + 0.293506i) q^{33} +(-1.27534 + 6.66742i) q^{35} +(2.24547 + 3.09062i) q^{37} +(0.548341 + 0.398393i) q^{39} +(1.48391 - 1.07813i) q^{41} +3.59445i q^{43} +(-5.61478 + 2.63868i) q^{45} +(4.56502 - 1.48326i) q^{47} -2.21619 q^{49} -0.883436 q^{51} +(9.03953 - 2.93712i) q^{53} +(3.05975 + 3.26158i) q^{55} -0.428989i q^{57} +(-8.61248 + 6.25734i) q^{59} +(-11.5481 - 8.39016i) q^{61} +(-4.95078 - 6.81417i) q^{63} +(1.35736 + 2.88829i) q^{65} +(-10.1670 - 3.30345i) q^{67} +(0.488588 - 1.50372i) q^{69} +(-3.85030 - 11.8500i) q^{71} +(0.157310 - 0.216518i) q^{73} +(2.36968 + 0.151474i) q^{75} +(-3.56882 + 4.91206i) q^{77} +(-2.64882 - 8.15223i) q^{79} +(2.16963 - 6.67743i) q^{81} +(12.0006 + 3.89923i) q^{83} +(-3.64411 - 2.00575i) q^{85} +(-1.10626 - 1.52263i) q^{87} +(-3.85736 - 2.80253i) q^{89} +(-3.50527 + 2.54673i) q^{91} -3.05836i q^{93} +(0.973973 - 1.76955i) q^{95} +(-9.47067 + 3.07721i) q^{97} -5.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} + q^{9}+O(q^{10}) \) 8 * q + 5 * q^3 + q^9	\( 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q + 5 * q^3 + q^9 + 4 * q^11 - 5 * q^13 - 15 * q^15 - 10 * q^17 + 5 * q^19 - 4 * q^21 - 5 * q^23 - 10 * q^25 + 5 * q^27 - 5 * q^29 + 9 * q^31 + 10 * q^33 - 15 * q^35 + 30 * q^37 + 3 * q^39 - 4 * q^41 - 15 * q^45 + 14 * q^49 + 4 * q^51 - 10 * q^53 + 10 * q^55 - 9 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 + 17 * q^69 - 6 * q^71 + 15 * q^73 + 10 * q^75 + 10 * q^77 - 15 * q^79 + 28 * q^81 + 45 * q^83 - 15 * q^85 + 20 * q^87 - 25 * q^89 - 6 * q^91 - 15 * q^95 - 60 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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